In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0.[1] Some start counting with 0, defining the natural numbers as the non-negative integers 0, 1, 2, 3, …, while others start with 1, defining them as the positive integers 1, 2, 3, … .[a] Some authors acknowledge both definitions whenever convenient.[2] Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the whole numbers refer to all of the integers, including negative integers.[3] The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1.
Yes. Some mathematicians think that 0 is natural, others don’t. So “natural number” is ambiguous.
In order to avoid ambiguity, instead of using fancy “N”, you should use fancy “N0” to refer to {0,1,2,3,4,…} and “positive integers” to refer to {1,2,3,4,…}.
Sauce
So it is undefined behavior, great
Yes. Some mathematicians think that 0 is natural, others don’t. So “natural number” is ambiguous.
In order to avoid ambiguity, instead of using fancy “N”, you should use fancy “N0” to refer to {0,1,2,3,4,…} and “positive integers” to refer to {1,2,3,4,…}.